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Totally Umbilical Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold

Khan, M. A., Uddin, Siraj, Singh, Khushwant (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 53C40, 53B25.In the present note we study totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold. We have obtained a classification theorem for totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold.

Totally umbilical submanifolds in some semi-Riemannian manifolds

Stanisław Ewert-Krzemieniewski (2010)

Colloquium Mathematicae

We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.

Traceless cubic forms on statistical manifolds and Tchebychev geometry

Hiroshi Matsuzoe (2005)

Banach Center Publications

Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.

Translation surfaces of finite type in Sol 3

Bendehiba Senoussi, Hassan Al-Zoubi (2020)

Commentationes Mathematicae Universitatis Carolinae

In the homogeneous space Sol 3 , a translation surface is parametrized by r ( s , t ) = γ 1 ( s ) * γ 2 ( t ) , where γ 1 and γ 2 are curves contained in coordinate planes. In this article, we study translation invariant surfaces in Sol 3 , which has finite type immersion.

Transversally symmetric immersions

José Carmelo González-Dávila, M. C. González-Dávila, Lieven Vanhecke (1997)

Mathematica Bohemica

We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.

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Masanori Adachi, Judith Brinkschulte (0)

Annales de l’institut Fourier

Willmore submanifolds in the unit sphere.

Guo Zhen (2004)

Collectanea Mathematica

In this paper we generalize the self-adjoint differential operator (used by Cheng-Yau) on hypersurfaces of a constant curvature manifold to general submanifolds. The generalized operator is no longer self-adjoint. However we present its adjoint operator. By using this operator we get the pinching theorem on Willmore submanifolds which is analogous to the pinching theorem on minimal submanifold of a sphere given by Simon and Chern-Do Carmo-Kobayashi.

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